Line Slope Intercept 54Daf1

1. **State the problem:** Find the slope-intercept form $y=mx+b$ of the line passing through points $(-5,-5)$ and $(1,-4)$. 2. **Formula for slope:** The slope $m$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1)=(-5,-5)$ and $(x_2,y_2)=(1,-4)$. 3. **Calculate the slope:** $$m=\frac{-4 - (-5)}{1 - (-5)}=\frac{-4 + 5}{1 + 5}=\frac{1}{6}$$ 4. **Use point-slope form:** $$y - y_1 = m(x - x_1)$$ Using point $(-5,-5)$: $$y - (-5) = \frac{1}{6}(x - (-5))$$ $$y + 5 = \frac{1}{6}(x + 5)$$ 5. **Simplify:** $$y + 5 = \frac{1}{6}x + \frac{5}{6}$$ 6. **Isolate $y$ to get slope-intercept form:** $$y = \frac{1}{6}x + \frac{5}{6} - 5$$ 7. **Simplify constant term:** $$y = \frac{1}{6}x + \frac{5}{6} - \frac{30}{6} = \frac{1}{6}x - \frac{25}{6}$$ 8. **Final answer:** The slope-intercept form is $$y = \frac{1}{6}x - \frac{25}{6}$$